New urn problem considers unknown sampling method.
problem Optimal stopping in urn sampling with unknown method.
method Continuous-time analog and bounds on value function.
result Optimal strategy same for balanced urn, surprising.
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48 results for “urn problem”
International Trade: a Reinforced Urn Network Modelphysics.soc-ph
We propose a unified modelling framework that theoretically justifies the main empirical regularities characterizing the international trade network. Each country is associated to a Polya urn whose composition controls the propensity of the country to trade with other countries. The urn composition is updated through t…
URN neural network dynamically generates various neural structures during training.
problem Creating neural networks with flexible, dynamic structures during training.
method Introduced Unstructured Recursive Network (URN) and used gradient descent on a single loss function.
result Different neural structures can emerge from a single URN during training.
The continuum-of-urns scheme, generalized beta and Indian buffet processes, and hierarchies thereofmath.PR
We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic …
We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian extensions, and the topic models such as the latent Dirichlet allocation. BAM is base…
Latent Dirichlet Allocation (LDA) is a topic model widely used in natural language processing and machine learning. Most approaches to training the model rely on iterative algorithms, which makes it difficult to run LDA on big corpora that are best analyzed in parallel and distributed computational environments. Indeed…
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size independent of the number of infected nodes. Our estimators are motivated by analogous …
New MAB model incentivizes user arm-pulling with self-reinforcing preferences.
problem Balancing exploration and exploitation in recommender systems with incentivized user preferences.
method Proposes a new MAB model with random arm selection and two policies: At-Least- Explore-Then-Commit and UCB-List.
result Achieves expected regret and expected payment over a time horizon .
This paper attempts to find out numerically the distribution of the queue-length ratio in the context of a model of preferential attachment. Here we consider two restaurants only and a large number of customers (agents) who come to these restaurants. Each day the same number of agents sequentially arrives and decides w…
We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-m…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …
Unsupervised Detection and Tracking of Arbitrary Objects with Dependent Dirichlet Process Mixturesstat.ML
This paper proposes a technique for the unsupervised detection and tracking of arbitrary objects in videos. It is intended to reduce the need for detection and localization methods tailored to specific object types and serve as a general framework applicable to videos with varied objects, backgrounds, and image qualiti…
International trade fluxes evolve as countries revise their portfolios of trade products towards economic development. Accordingly products' shares in international trade vary with time, reflecting the transfer of capital between distinct industrial sectors. Here we analyze the share of hundreds of product categories i…
The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an ordered block model. That is, the nodes of the graph are objects which fall into …
Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Monthsphysics.soc-ph
We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the ana…
Elicitation without Backpropagation: Steering Model Behavior by Optimizing the Latent Posteriorcs.LG
PPT optimizes transformer behavior by steering its latent posterior using prior samples.
problem Eliciting desired behavior from transformers without backpropagation.
method Posterior Prefix Tuning (PPT) uses predictive Monte Carlo (PMC) samples and importance sampling to optimize the latent posterior.
result PPT optimizes transformer behavior without backpropagation, achieving high utility across different utility functions.
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is necessarily either dens…
Survey on Bayesian inference for Gaussian mixture models.
problem Estimating parameters of Gaussian mixture models using Bayesian methods.
method Uses Bayesian inference to estimate parameters and uncertainty of Gaussian mixture models.
result Bayesian approach provides point estimates and associated uncertainty for mixture model parameters.
We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold gr…
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
Solves four problems related to circle families in the plane.
problem Four basic problems of circle families in the plane.
method Solves all four basic problems of circle families in the plane.
result All four basic problems are solved.
Solves four problems related to sphere families in 3D space.
problem Four basic problems of sphere families in Euclidean 3-space.
method Solves all four basic problems of sphere families in Euclidean 3-space.
result All four basic problems are solved.
Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometrymath.OC
The paper solves optimal control problems for various convex sets using convex trigonometry.
problem Optimal control problems with 2D convex compact sets.
method Using convex trigonometry to derive extremals for various problems.
result Geodesics in multiple sub-Finsler problems are derived.
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…
This paper solves the Christoffel problem in hyperbolic space and its equivalent on spheres.
problem Prescribing curvatures for convex hypersurfaces in hyperbolic space.
method Proving a full rank theorem to establish the existence of solutions.
result Existence of solutions to the Christoffel problem and its equivalent Nirenberg-Kazdan-Warner problem on spheres.
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we anal…
Study proves only origin-centered spheres solve certain curvature problems.
problem Proving uniqueness of solutions to curvature problems.
method Using the Heintze-Karcher inequality, the study proves the uniqueness of smooth, strictly convex solutions to a class of Minkowski type problems.
result Only origin-centered spheres solve isotropic and -Gaussian-Minkowski problems.
MathChat uses LLM agents to solve challenging math problems through conversational problem-solving.
problem Solving math problems expressed in natural language.
method MathChat is a conversational framework combining an LLM agent and a user proxy agent for collaborative problem-solving.
result MathChat improves tool-using prompting methods by 6% on difficult math problems.
The paper solves a generalized Christoffel-Minkowski problem using a curvature flow.
problem Solving the (p,q)-Christoffel-Minkowski problem.
method Investigating the problem via an expanding curvature flow.
result Existence and uniqueness of smooth solutions to the (p,q)-Christoffel-Minkowski problem.
Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spacesmath.OC
Paper solves Gromov-Wasserstein for point clouds efficiently.
problem Quantifying similarity between two formations or shapes.
method Reformulates QAP as low-rank concave quadratic optimization problem.
result Global solution for large-scale problems with thousands of points.
The paper explains how microlocal analysis solves geometric inverse problems.
problem Recovering geometric information from boundary measurements.
method Microlocal analysis applied to three inverse problems.
result Microlocal techniques solve specific inverse problems in Riemannian geometry.
Proves NP and co-NP status for knot core recognition in solid torus.
problem Determining if a knot is the core of a solid torus.
method Alternate proof and corollary of Hopf link recognition problem.
result Proves NP and co-NP status for solid torus core recognition problem.
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal processing and communication (SPCOM) problems. Despite its popularity, most exist…
A Decomposition Method for LQ Conditional McKean-Vlasov Control Problems with Random Coefficientsmath.OC
A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
Some group theory problemsmath.GR
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary definitions and motivations, problems and some discussions of them. For ea…
We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric problems about (almost) complex structures, both algebraic and non-algebraic, about co…
New method solves generalized Minkowski problem for torsional rigidity.
problem Generalized Minkowski problem for torsional rigidity.
method Flow method
result Existence of solutions for general measures.
We present 27 problems encountered in automating the translation of movie/TV show subtitles. We categorize each problem in one of the three categories viz. problems directly related to textual translation, problems related to subtitle creation guidelines, and problems due to adaptability of machine translation (MT) eng…
Solves Brezis' first open problem on ball solutions.
problem Existence of solutions to Brezis-Nirenberg problem on a 3D ball.
method Building on sign-changing solutions to the Yamabe problem.
result Infinitely many sign-changing, nonradial solutions found.
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking or media memorability. In this article, we systematically review different types…
Classical knot recognition problem solved in NP with exponential time algorithm.
problem Determining if a virtual knot is classical.
method Proved NP membership and provided an exponential time algorithm.
result Classical knot recognition problem is in NP.
Paper solves four problems of pseudo-circle envelopes in Minkowski plane.
problem Four problems of pseudo-circle envelopes in Minkowski plane.
method Solutions to four basic problems.
result Solved four problems of pseudo-circle envelopes in Minkowski plane.
In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum likelihood estimation. The exact treatment of maximum likelihood estimation is intra…
Conference compiles problems on foliations and diffeomorphisms.
problem Challenges in foliations and diffeomorphism groups.
method Compilation of problems from conference participants.
result Compilation of 20+ problems on foliations and diffeomorphisms.
Describes state variables in sequential decision problems, linking them to Markovian and non-Markovian models.
problem Sequential decision problems, especially in active learning and POMDPs, where decisions affect what is observed and learned.
method Canonical framework and novel two-agent perspective of POMDPs, defining state variables to claim Markovian or non-Markovian models.
result Properly modeled sequential decision problems are Markovian, while real decision problems are often non-Markovian.
Solves double coset problem for braid group H_n.
problem Double coset problem in braid group B_n modulo H_n.
method Uses Garside's decomposition of braids in B_n.
result Demonstrates stable equivalence of Link Problem to solvable algebraic problem.
This paper solves the dual Minkowski problem for q-torsional rigidity.
problem The dual Minkowski problem for q-torsional rigidity.
method Introduced the p-th dual q-torsional measure and solved the p-th dual Minkowski problem for q-torsional rigidity using a Gauss curvature flow.
result Existence of smooth even and non-even solutions to the p-th dual Minkowski problem for q-torsional rigidity.
In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the proof, the problem is reduced to an inverse source problem for a kinetic equation …